Large-Scale Estimation under Unknown Heteroskedasticity
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918081087930368 |
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| author | Ho, Sheng Chao |
| author_facet | Ho, Sheng Chao |
| contents | This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^κ/ n$. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02293 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-Scale Estimation under Unknown Heteroskedasticity Ho, Sheng Chao Econometrics This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of heterogeneous parameters, such as unit-specific means or quantiles, in terms of the density of certain sufficient statistics. These are used to propose feasible versions with nearly parametric regret bounds of the order of $(\log n)^κ/ n$. The estimators are employed in a study of teachers' value-added, where we find that allowing for heterogeneous variances across teachers is crucial for delivery optimal estimates of teacher quality and detecting low-performing teachers. |
| title | Large-Scale Estimation under Unknown Heteroskedasticity |
| topic | Econometrics |
| url | https://arxiv.org/abs/2507.02293 |